Finite Group Databasebeta

← Group #499367

Character table — Group #499367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112222222224448888888888881616161616161616112222222224448888888888881616161616161616
order122224444888884488161616161616161622448888222224444888884488161616161616161622448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ611111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ711111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ9222222222-2-2-2-2-222-2-20000000000000000222222222-2-2-2-2-222-2-20000000000000000
χ10222222222-2-2-2-2-2-2-2220000000000000000222222222-2-2-2-2-2-2-2220000000000000000
χ1122222-2-2-2-200000002i−2ii2i2−i2−i222−2−20000000022222-2-2-2-200000002i−2ii2i2−i2−i222−2−200000000
χ1222222-2-2-2-200000002i−2i−i2−i2i2i2−2−2220000000022222-2-2-2-200000002i−2i−i2−i2i2i2−2−22200000000
χ1322222-2-2-2-20000000−2i2ii2i2−i2−i2−2−2220000000022222-2-2-2-20000000−2i2ii2i2−i2−i2−2−22200000000
χ1422222-2-2-2-20000000−2i2i−i2−i2i2i222−2−20000000022222-2-2-2-20000000−2i2i−i2−i2i2i222−2−200000000
χ15222-2-22-22-2000002i−2i002−22−2i2−i2i2−i200000000222-2-22-22-2000002i−2i002−22−2i2−i2i2−i200000000
χ16222-2-22-22-2000002i−2i00−22−22−i2i2−i2i200000000222-2-22-22-2000002i−2i00−22−22−i2i2−i2i200000000
χ17222-2-22-22-200000−2i2i002−22−2−i2i2−i2i200000000222-2-22-22-200000−2i2i002−22−2−i2i2−i2i200000000
χ18222-2-22-22-200000−2i2i00−22−22i2−i2i2−i200000000222-2-22-22-200000−2i2i00−22−22i2−i2i2−i200000000
χ19222-2-2-22-22222-2-2000000002i−2i−2i2i00000000222-2-2-22-22222-2-2000000002i−2i−2i2i00000000
χ20222-2-2-22-22222-2-200000000−2i2i2i−2i00000000222-2-2-22-22222-2-200000000−2i2i2i−2i00000000
χ21222-2-2-22-22-2-2-22200002i−2i−2i2i000000000000222-2-2-22-22-2-2-22200002i−2i−2i2i000000000000
χ22222-2-2-22-22-2-2-2220000−2i2i2i−2i000000000000222-2-2-22-22-2-2-2220000−2i2i2i−2i000000000000
χ2322-22-222-2-222-22-2000000000000002i−2i000022-22-222-2-222-22-2000000000000002i−2i0000
χ2422-22-222-2-222-22-200000000000000−2i2i000022-22-222-2-222-22-200000000000000−2i2i0000
χ2522-22-222-2-2-2-22-220000000000000000002i−2i22-22-222-2-2-2-22-220000000000000000002i−2i
χ2622-22-222-2-2-2-22-22000000000000000000−2i2i22-22-222-2-2-2-22-22000000000000000000−2i2i
χ2722-2-22-222-222-2-220000000000002-200000022-2-22-222-222-2-220000000000002-2000000
χ2822-2-22-222-222-2-22000000000000-2200000022-2-22-222-222-2-22000000000000-22000000
χ2922-2-22-222-2-2-222-200000000000000002i−2i0022-2-22-222-2-2-222-200000000000000002i−2i00
χ3022-2-22-222-2-2-222-20000000000000000−2i2i0022-2-22-222-2-2-222-20000000000000000−2i2i00
χ3144-44-4-4-444000000000000000000000000044-44-4-4-4440000000000000000000000000
χ3244-4-444-4-44000000000000000000000000044-4-444-4-440000000000000000000000000
χ338-8000000042−42000000000000000000000008-8000000042−4200000000000000000000000
χ348-80000000−4242000000000000000000000008-80000000−424200000000000000000000000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ37111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ38111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ3911111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ4011111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ4111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4211111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ43222222222-2-2-2-2-222-2-20000000000000000-2-2-2-2-2-2-2-2-222222-2-2220000000000000000
χ44222222222-2-2-2-2-2-2-2220000000000000000-2-2-2-2-2-2-2-2-22222222-2-20000000000000000
χ4522222-2-2-2-200000002i−2ii2i2−i2−i222−2−200000000-2-2-2-2-222220000000−2i2i−i2−i2i2i2−2−22200000000
χ4622222-2-2-2-200000002i−2i−i2−i2i2i2−2−22200000000-2-2-2-2-222220000000−2i2ii2i2−i2−i222−2−200000000
χ4722222-2-2-2-20000000−2i2ii2i2−i2−i2−2−22200000000-2-2-2-2-2222200000002i−2i−i2−i2i2i222−2−200000000
χ4822222-2-2-2-20000000−2i2i−i2−i2i2i222−2−200000000-2-2-2-2-2222200000002i−2ii2i2−i2−i2−2−22200000000
χ49222-2-22-22-2000002i−2i002−22−2i2−i2i2−i200000000-2-2-222-22-2200000−2i2i00−22−22−i2i2−i2i200000000
χ50222-2-22-22-2000002i−2i00−22−22−i2i2−i2i200000000-2-2-222-22-2200000−2i2i002−22−2i2−i2i2−i200000000
χ51222-2-22-22-200000−2i2i002−22−2−i2i2−i2i200000000-2-2-222-22-22000002i−2i00−22−22i2−i2i2−i200000000
χ52222-2-22-22-200000−2i2i00−22−22i2−i2i2−i200000000-2-2-222-22-22000002i−2i002−22−2−i2i2−i2i200000000
χ53222-2-2-22-22222-2-2000000002i−2i−2i2i00000000-2-2-2222-22-2-2-2-22200000000−2i2i2i−2i00000000
χ54222-2-2-22-22222-2-200000000−2i2i2i−2i00000000-2-2-2222-22-2-2-2-222000000002i−2i−2i2i00000000
χ55222-2-2-22-22-2-2-22200002i−2i−2i2i000000000000-2-2-2222-22-2222-2-20000−2i2i2i−2i000000000000
χ56222-2-2-22-22-2-2-2220000−2i2i2i−2i000000000000-2-2-2222-22-2222-2-200002i−2i−2i2i000000000000
χ5722-22-222-2-222-22-2000000000000002i−2i0000-2-22-22-2-222-2-22-2200000000000000−2i2i0000
χ5822-22-222-2-222-22-200000000000000−2i2i0000-2-22-22-2-222-2-22-22000000000000002i−2i0000
χ5922-22-222-2-2-2-22-220000000000000000002i−2i-2-22-22-2-22222-22-2000000000000000000−2i2i
χ6022-22-222-2-2-2-22-22000000000000000000−2i2i-2-22-22-2-22222-22-20000000000000000002i−2i
χ6122-2-22-222-222-2-220000000000002-2000000-2-222-22-2-22-2-222-2000000000000-22000000
χ6222-2-22-222-222-2-22000000000000-22000000-2-222-22-2-22-2-222-20000000000002-2000000
χ6322-2-22-222-2-2-222-200000000000000002i−2i00-2-222-22-2-2222-2-220000000000000000−2i2i00
χ6422-2-22-222-2-2-222-20000000000000000−2i2i00-2-222-22-2-2222-2-2200000000000000002i−2i00
χ6544-44-4-4-4440000000000000000000000000-4-44-4444-4-40000000000000000000000000
χ6644-4-444-4-440000000000000000000000000-4-444-4-444-40000000000000000000000000
χ678-8000000042−4200000000000000000000000-880000000−424200000000000000000000000
χ688-80000000−424200000000000000000000000-88000000042−4200000000000000000000000

Here i is the imaginary unit (i² = −1).